Math 221 Ė Principles of Statistics

Examples of Scatterplots and Their Correlation Coefficients (Pearsonís)


Here are some scatterplots, with Pearsonís correlation coefficients and interpretations. Look them over and get a feel for what the coefficient tells you.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Some see no association in this scatterplot at all, your author included. Some say thereís a weak positive association, but if you remove the unusual point in the upper-right corner, that impression seems to disappear. Some say thereís a weak negative association, but that impression is seriously strengthened by the removal of the unusual point in the upper-right corner. If there really is a pattern in the data, its existence should not depend so heavily on a single point! (If you're curious, ).


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Thereís a fairly strong, positive association here, but itís definitely not linear! So you shouldnít use  with these data, at all. Itíll be biased.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

There seems to be a positive association here, but itís too weak to determine visually whether itís linear. However, there are those who would be willing to give it the benefit of the doubt. For their sake, we calculate      to be 0.726. Note that this moderately high value does not (by itself) imply that there is a linear association.

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

There is a clear negative association, but it may not be strictly linear. There seems to be some curvature to it. The use of  here is a bit risky, but not terribly so, since the data are only slightly curved. It turns out that is --0.916.

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This scatterplot is for the same data as the previous one, but with the axes interchanged. Notice that the negativity of the association is still evident. Soóas far as the strength and direction of the association are concernedóit doesnít matter which variable goes on which axis. This is confirmed by the fact that is --0.916, just as in the previous example.

 

 

SPSS instructions for calculating Pearsonís correlation coefficient: Click here.

 

Related topics:

 

Scatterplots

 

Testing claims about Pearsonís correlation coefficient

 

Simple linear regression

 

Exploratory data analysis

 

Statistics reference page: Click here.

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David E. Brown

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